Non-linear least squares fitting of coefficients in the Herschel–Bulkley model

The Herschel–Bulkley model can be used to describe the rheological behaviour of certain non-Newtonian fluids. When fitting to experimental data, its parameters need to be determined and this is a non-linear problem. The conventional approach is to solve the resulting normal equations numerically. An alternative method is presented for the Herschel–Bulkley model which eliminates the complexity associated with a general numerical method, and so offers potential benefits when dealing with the model in practice.